I've been keeping my little Michael's acrylic stamps on a scrapper's ring. Each pkg has a nice hanging hole at the top for the ring to go through and the pkg opens at the other end so you don't even have to remove the set from the ring to use it.
I have "like stamps" on the same ring - thank you, thinking of you, special occasion. The loaded rings are tossed in a small drawer and are easy to grab and use without a lot of fuss. It's not a high tech solution, but is very user friendly!
P.S. For those who don't know what a scrapper's ring is, it is a metal ring that opens easily and latches securely in a little notch. They come in many sizes but my favorite is the 1 1/4" size because they hold a lot of pkgs of stamps. You can usually buy these individually at a scrap store for about 35 cents or in a package about $4(?).